The compression rate of image data has increasingly become an important issue as computer graphics is widely used. To compress image data, subband encoding techniques are generally accepted and include Discrete Cosine Transform (DCT) and Wavelet Transform. In general, the subband image coding techniques rely upon the representation that image display signals for representing lower frequency regions of an image have stronger electrical power that those representing higher frequency regions. Since the lower frequency regions contain more visual information, the larger number of bits is assigned to represent the lower frequency regions. These encoding techniques are generally applied to a predetermined number of image-blocks, and to compress the image data information, a portion of each block is assigned a predetermined number of bits based upon the frequency in the portion. To determine the frequency in the portion, a frequency filter of a predetermined characteristics is used. In general, please see for example, Wavelet Transforms, Chapter 6, Principles of Digital Image Synthesis, Vol One, Glassner (1995).
Among the above described encoding techniques, the wavelet transform appears to be desirable for compressing image data. To be desirable in compressing digital data, a basis expression of filters should be discrete and orthogonal. One example of such filters includes the Haar basis. Using these filters, the wavelet transform provides multi resolution expressions and a zonally variable basis. In other words, as the wavelet transform is recursively repeated, the resolution is reduced by half. In addition, the band dividing characteristic of the filters used in the wavelet transform allows octave divisions. In contrast to these advantages, DCT does not provide the above described advantageous filter characteristics. "Subband encoding and Wavelet Transform," in Japanese, Interface, August (1992).
Despite the above described advantages of the wavelet transform-based compression technique, due to the increased use of computer graphics, the compression rate is desired for improvement especially for large image data.